Problem: If $x \odot y = 6x+y$ and $x \barwedge y = 4x-2y$, find $(3 \barwedge 3) \odot 2$.
Solution: First, find $3 \barwedge 3$ $ 3 \barwedge 3 = (4)(3)-(2)(3)$ $ \hphantom{3 \barwedge 3} = 6$ Now, find $6 \odot 2$ $ 6 \odot 2 = (6)(6)+2$ $ \hphantom{6 \odot 2} = 38$.